The study of Cartan C*-subalgebras, initiated by Kumjian and Renault several decades ago, has led to numerous advances in the classification and representation theory of C*-algebras. In particular, Renault showed in 2008 that the presence of a Cartan subalgebra guarantees that a C*-algebra has a dynamical representation via a topologically principal twisted groupoid. We identify a class of non-topologically principal groupoids that give rise to twisted groupoid C*-algebras admitting Cartan subalgebras generated by certain abelian subgroupoids. By Renault's theorem, these algebras can also be modeled by topologically principal twisted groupoids. In the special case that the original groupoid is a discrete group G, we further describe the relationship between G and the groupoid arising from application of Renault's theorem.

This is joint work with Anna Duwenig, Rachael Norton, Elizabeth Gillaspy, and Sarah Wright.